Deduce expressions to calculate the nth term of quadratic and cubic sequences.

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This is level 3; Quadratic sequences of the form an2 + bn + c. You can earn a trophy if you get at least 5 questions correct.

 Find the nth term of the sequence:7, 15, 25, 37, 51, 67, ... Working: Find the nth term of the sequence:9, 18, 29, 42, 57, 74, ... Working: Find the nth term of the sequence:13, 26, 41, 58, 77, 98, ... Working: Let $$f$$ be a quadratic function with:$$f(1) = 0, f(2) = 4 \text{ and } f(3) = 10$$.Determine $$f(8)$$. Working: Find the nth term of the sequence:0, -9, -22, -39, -60, -85, ... Working: The first three terms of a quadratic sequence are 24, 30, 38. Which term is equal to 128? Working: The first three terms of a quadratic sequence are 15, 20, 27. Which term is equal to 155? Working:
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This is Quadratic and Cubic Sequences level 3. You can also try:
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Polygon Pieces

Arrange the nine pieces of the puzzle on the grid to make the given polygon. Level one is for those learning the names of shapes while other levels are for those who like a challenge!

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Thursday, January 20, 2022

"Have you seen the Leapfrog investigation? It's a challenge to find the minimum number of moves to swap the positions of the blue and green frogs by encouraging them to leap from one lily pad to another. The investigation will reveal a quadratic sequence but can you find the rule for the nth term? The investigation has been cunningly named Leapfrog. Have a look!"

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Description of Levels

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Level 1 - Quadratic sequences of the form n2 + c

Level 2 - Quadratic sequences of the form an2 + c

Level 3 - Quadratic sequences of the form an2 + bn + c

Level 4 - Quadratic sequence problem solving

Level 5 - Cubic sequences of the form an3 + bn2 + cn + d

Exam Style questions are in the style of GCSE exam paper questions and worked solutions are available for Transum subscribers.

Handshakes - Try this lesson Starter which can generate a quadratic number sequence.

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